Abstract and Applied Analysis

Algebraic Structures Based on a Classifying Space of a Compact Lie Group

Dae-Woong Lee

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Abstract

We analyze the algebraic structures based on a classifying space of a compact Lie group. We construct the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products, and we show that the homomorphic image of homology generators can be expressed in terms of the Lie brackets in rational homology. By using the Milnor-Moore theorem, we also investigate the concrete primitive elements in the Pontrjagin algebra.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 508450, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393444210

Digital Object Identifier
doi:10.1155/2013/508450

Mathematical Reviews number (MathSciNet)
MR3126732

Zentralblatt MATH identifier
1292.55006

Citation

Lee, Dae-Woong. Algebraic Structures Based on a Classifying Space of a Compact Lie Group. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 508450, 7 pages. doi:10.1155/2013/508450. https://projecteuclid.org/euclid.aaa/1393444210


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